Integrated power and linewidth of a propagating and a self-localized spin wave modes excited by spin-polarized current in an obliquely magnetized magnetic nanocontact are studied experimentally as functions of the angle θe between the external bias magnetic field and the nanocontact plane. It is found that the power of the propagating mode monotonically increases with θe, while the power of the self-localized mode has a broad maximum near θe = 40 deg, and exponentially vanishes near the critical angle θe = 58 deg, at which the localized mode disappears. The linewidth of the propagating mode in the interval of angles 58 < θe < 90 deg , where only this mode is excited, is adequtely described by the existing theory, while in the angular interval where both modes can exist the observed linewidth of both modes is substantially broadened due to the telegraph switching between the modes. Numetical simulations and an approximate analytical model give good semiquantitative description of the observed results.